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2008 Toyota Rav4 • 4 cylinder 4WD Automatic • 45,000 miles

I own a 2008 RAV4 whose engine has been running rough lately and the start takes a little longer and it seems sometimes that is not going to work. It has also lost power when accelerating and sometimes you can feel the engine vibration more than you should when iddling. I have also noticed that it is giving me less miles per fuel tank than before. Battery was changed a couple of weeks ago at the dealer's and they told me that was going to fix the issue, but it didn't. Do you have any ideas as of what the issue may be.
Thanks in advance.
-Jorge O.